Urban travel alternatives: Models for individual and collective preferences

URBAN TRAVEL ALTERNATIVES: MODELS FOR INDIVIDUAL AND COLLECTIVE PREFERENCES JOHN ODLAND and JOHN JAKUBS Department of Geography, Indiana University, Bloomington. IN 47401,U.S.A. (Received 4 February 1977)

Ahstraet-A method of estimating preference functions for alternative urban travel modes using non-metric scaling and conjoint measurement is introduced. The method treats travel alternatives as alternative collections of generic attributes and disaggrcgales preference orderings for alternative modes into components associated with the generic attributes. Preference functions are fitted for individual respondents and alternative methods of estimating collective preference functions for the group of respondents are examined. Particular attention is given to the error associated with aggregating individual responses. The methods are designed to bc effective with relatively modest quantities of surrey data.

New demands have been placed on urban transportation planning methods because of reorientations of policy which favor technological innovation in transit modes and introduction of public transit into places where it has not been available. Most of the commonly used methods of predicting travel demand or mode choice amount to projections of existing behavior based on aggregate data. These methods work well in projecting responses to minor system changes but they are not well-suited to predict responses to innovations or major system changes. If major changes occur there may be no established behavior pattern that can provide a reliable basis for projection. Alternatives to aggregate-level analysis are offered by the disaggregate behavioral models which are receiving an increasing proportion of the total effort in urban transportation research [ l-51. These models are adapted to explain the choice-making of individual transit users but they are not designed to provide the aggregate-level projections which are usually required for planning decisions. Improved understanding of the individual travel decision is probably a prerequisite to effective modelling of the consequences of transit innovations or major system changes but improved understanding of individual behavior wili contribute little to planning predictions unless it can be related to aggregatelevel behavior. The set of methods discussed in this paper is especially useful for constructing models of individual preferences for transit alternatives and relating them to aggregate-level counterparts. The models are constructed along lines suggested by Lancaster’s theory of consumer demand~4~71.This theory implies that preference orderings for a set of transportation alternatives are derived from attributes, such as speed, comfort, and service frequency. which are offered in varying amounts by particular transit alternatives such as commuter trains or private automobiles. Models of individual choice-making are based on observed relations between preference orderings for transit alternatives and the attributes possessed by the alternatives. Coefficients which describe these relations can be obtained by preference scaling and conjoint measurement [8,9] applied to pairwise choices among alternatives as made by individual transit users.

The result is a model of individual preferences. Parallel models can be constructed on the basis of data aggregated at the level of individual pairwise choices or at the level of individual preference functions. The result of aggregation at either levei is a model of collective preferences which is directly comparable with models of individual preferences. Alternative methods of estimating models of collective preferences are discussed in the following sections. Empirical results for the various methods are compared on the basis of sample data collected in a survey of rail commuters in certain North Shore suburbs of Chicago. Special attention is given to the question of whether a single preference function can provide an adequate representation of choices made by the entire sample of respondents. DISA(;GREGATED TRAiXStT PREFEREWCES

Disaggregation of urban travel alternatives into component attributes is the crucial element in the models presented here. Urban travel alternatives are treated as “bundles” of generic attributes and a preference ordering for alternative bundles is derived as a joint effect of preferences for the generic attributes associated with each bundle. Each alternative is assumed to derive its position in a preference ordering solely from the set of generic attributes which it offers in a particular combination. Conjoint measurement provides a method of identifying a composition rule which explains the preference ordering as a joint effect of the generic attributes. Several advantages are associated with the treatment of transit alternatives as aggregations of generic attributes. In particular, the response to innovations or major system changes can be projected in terms of the generic attributes rather than projecting responses to alternatives. The attributes are more general than the particular combinations which exist as transit alternatives and the response to an innovative or previously unavailable mode may be projected by treating it as a new combination of attributes provided that a composition rule exists which can assign the new combination a position in a preference ordering. A general theoretical framework for analysis of transit choice behavior in terms of generic attributes is provided 265

166

JOHN O~r.nsn

by Lancaster’s theory of consumer demand. This approach was pioneered in transportation analysis[ lo] and has been applied previously to problems of mode choice [ 1I, 121. Lancaster argues that people purchase goods in order to obtain attributes or “characteristics” which are offered in particular combinations by various goods. The relation between a set of goods and the associated set of attributes is given by the relation z=Bx where z is a vector of generic attributes, x is a vector of quantities of goods and B is called the “consumption technology matrix”. Elements of one row of B are quantities of a particular attribute which are offered by unit quantities of each good. The consumer choice problem is to select the optimal set of goods subject to this relation and the limits of a fixed income. The choice problem can be formalized as the mathematical programming problem: maximize

U = U(z),

(1)

subject to

z = Bx,

(2)

px< Y,

(3)

x Z-0,

(4)

where U(z) is a utility function defined over attributes; p is a vector of prices; and Y is the fixed income. This general approach to demand theory has the capacity to yield more informative models than the traditional theory, which treats goods as atomistic. The formulation in eqns (l)-(4) contains information, in the matrix B, about the properties of goods as well as information about preferences. Traditional demand theory incorporates only information about preferences. Further, there are special features of the transit choice problem which set it apart from most consumer choice but which make Lancaster’s demand theory especially appropriate. First, the selection of a set of trips can be analyzed independent of the prices of other goods. Trip-making is, as Button notes [ 13, p. 631, an “intrinsic group” of goods the efficient selection of which is separable from other kinds of consumption because the desired characteristics of trips can be obtained only by making trips and tripmaking cannot provide characteristics which are associated with other goods. Technically, this means that the B matrix can be permuted into a matrix of the form B, c0

0 B, I

where the submatrix B, is a consumption technology matrix for trip-making and B, is a consumption technology matrix for other goods. Practically, it means that changes in the prices of goods other than travel do not affect the optimum consumption of trips. This does not conflict with the usual assertion that the demand for transportation is derived from the demand for other goods. Rather, it means that once a demand for travel is established, from whatever source, the efficient selection of a set of trips is independent of the prices of other goods. Second, the choice of transportation alternatives is set apart from most consumer choices by the limited nature of the choice set which confronts most decision makers.

and JOHN JAKW

Persons making transportation decisions generally are faced with a finite number of alternatives which offer a few distinct combinations of the various attributes. This means, in formal terms, that the choice space consists of a finite number of isolated points rather than a continuous range of possibilities. Consequently, the usual marginal analysis of consumer choice is not available for individuals although rationalizations based on variations in tastes can restore the possibility of marginal analysis for populations of consumers [ 141. Demand analysis for the case of finite alternatives is, however, readily handled by Lancaster’s theoryl7, pp. SO-71]. Operational models of transit choice based on the notion of disaggregated preferences can be defined using fairly modest quantities of sample data. Conjoint measurement provides a method of defining a utility index for each transit alternative as a joint effect of its abstract attributes. The utility indices provide a basis for predicting individuals’ transit choices while the associated coefficients indicate the contribution of each attribute to the total utility value for the alternative. Pragmatic considerations favor pairwise choices or pairwise preferences among alternatives as the basic units of data. Models of individual preferences and choice behavior often require extensive data sets gathered in individual interviews and this limits the application of the models in situations where the behavior of large, and possibly varied, populations must be represented. Data on pairwise choices and pairwise preferences are more readily obtained in very brief interviews than are responses to alternative modes of questioning such as category ratings or ranking tasks. Additionally, data in the form of pairwise choices may be obtained by observation of revealed behavior as well as by query. Pairwise choices have the disadvantage that the number of choices increases as the square of the number of alternatives. It is not always necessary, however, to elicit responses to all possible pairs. A dominance assumption is used in this research to reduce the choices to a number that can be obtained by means of a very brief questionnaire. Finally, models should be adaptable to the analysis of collective as well as individual behavior. as mentioned above. The models developed here handle individual and collective preferences in the same structural form and make it possible to evaluate the error associated with aggregation. INDrVlDUAL Ah-D COLLECTIVE PREFERENCES

Models of preference structures can be obtained by analyzing the rank orderings of alternatives implied by sets of pairwise choices between transportation alternatives. The rationale for models of collective preference follows from the models for individual preference. A model of indicidual preferences A preference ordering for an individual can be constructed where the individual is confronted with a set of transportation alternatives and is able to select one member of each pair of alternatives as preferred to the other. An internal preference scaling algorithm such as MDPREF[l5] can be used to recover the rank ordering of alternatives which corresponds to an individual’s set of pairwise choices. In accordance with the Lancaster model, we assume that the pairwise choices and the associated rank orderings depend on the values of a set

Urban

travel

alternatives:

models

for individual

of attributes associated with each alternative. Let the series (Xri, xzi, . .,x.,) be the values of n attributes representing alternative i. The attributes could be qualities such as speed, comfort. and service frequency, while the alternative is a particular mode, such as commuter train, which offers these qualities in a particular combination of amounts. A second alternative, such as auto travel for the same trip, would offer the same qualities in different amounts. The individual’s preferences for travel alternatives are representable if a real-valued function such that the value of s(x*. x2,. . .,x,1 exists S(X,I,XZ,,. . ., x,,) exceeds the value of s(xli, x2,, . . .I X”i) whenever alternative i is preferred to alternative j. Conjoint measurement provides methods for determining composition rules, such as s(xI,x2,. . ., x,,), which measure the joint effect of two or more independent variables on a dependent variable. Many such methods are available for ratio-scaled data but conjoint measurement requires only ordinal information. The information on the dependent variable, in the case of transportation preferences, is a rank ordering of the transportation alternatives. The independent variables are the generic attributes such as speed or user cost. These may take on a fixed set of values rather than a continuous range. Conjoint measurement simultaneously determines a ratio-valued preference scale for the alternatives and a combination rule which identifies the value of each alternative on that scale on the basis of the values of its attributes. The conjoint measurement routine used in this analysis is MONANOVA[l6], which has the same format as an additive main effects analysis of variance. The routine is appropriate for models which can be represented as full factorial designs or as designs, such as Latin-squares, which are embedded in a full factorial design. The algorithm determines coefficients 2(x&), one for each level of each attribute, such that the sum of coefficients for the set of attributes corresponding to an alternative is monotonically related to the rank ordering of the alternatives. The set of coefficients amounts to a model of preferences since the z(x~) values can be interpreted as partial utilities measuring the contribution to the total utility of a particular level of a particular attribute. Collectice preferences Aggreguting puirwise

choices. Models of collective preference can be obtained by aggregation at the level of individual pairwise choices or at the level of individual preference functions. Models constructed by aggregation at the level of pairwise choices replicate the full process of fitting the individual models. Individual choices are aggregated to form distance measures between the pairs of alternatives in a choice space. The distance between alternatives can be proportional to the percentage of the population which chooses the more popular member of a pair. Preference scaling can recover an ordering of the alternatives on the basis of these distances and conjoint measurement can be used to identify a combination rule based on levels of attributes offered by each alternative. An equation which can be used to generate distances in a choice space on the basis of individual pairwise choices is:

d,, =

1(VI’ 2 P,,,) - 0.51.

where the summation is over m individuals and piik is a

267

and collective preferences

binary variable which has a value of one when i is preferred to j by individual k and zero otherwise. There are some advantages to aggregation at the level of pairwise choices. Distances can be calculated without eliciting choices from all respondents. In fact, the choices may be inferred from revealed behavior rather than from questioning. However, formulas for calculating distances in the choice space are derived from Thurstone’s Law of Comparative Judgment and require that preferences be homogeneous over the set of respondents. The distances which form the basic data for scaling are meaningless if the population contains two or more groups whose preferences differ in significant ways. There is no sure means of establishing uniformity without examining individual preferences. Aggregating tions. Aggregation

indicidual

preference

func-

at the level of individual preference functions requires more extensive data for each individual but it does allow examination of hypotheses about the homogeneity of preferences. When heterogeneous preferences are present, the population may be disaggregated into internally homogenous groups or the aggregation method may employ weights to minimize the effect of deviant individuals on the collective preference function. Coefficients for a collective preference function may be obtained as averages or weighted averages of the corresponding coefficients in individual functions. A suitable operation is:

Z(Xi) =

c WkZk(X,).

where Z(xi) is the coefficient of a collective function, the summation is over M individuals, and We is a weight associated with individual k. The We values may be used in several ways in order to cope with the presence of heterogeneous preferences. They may be binary values which are non-zero only when the individual is a member of a predetermined group. In this case, separate collective preference functions are obtained for each group. The wk values also may be used to minimize the effect of deviant individuals when a single preference function is calculated. The weights may depend on characteristics of the individual which are treated as external to his preferences, such as travel frequency, or they may depend on the difference between his individual zl(x,) value and a measure of the central tendency of all z(x,) values. This type of weighting reduces the effect of deviant individuals on the collective function. Eaaluating

models

of collectice

preferences

A straightforward way to evaluate a model of collective preference is to compare its success in predicting pairwise choices with that of individual models applied to members of the same population. The proportion of incorrectly predicted pairwise choices provides only a partial evaluation of the models since the failure of a collective model to predict correctly all the pairwise choices made by a population can have two sources. First, a stimulus may not always evoke the same response from an individual. or from two individuals with identical preference scales; second, the aggregated population may COnktin a mixture of individuals whose varied preferences cannot be represented by a single scale. Pairwise choices may be predicted incorrectly because of random variation in responding to stimuli even in

268

JOHN ODLAND

and JOHN

cases where all individuals in the population share identical preferences. Thurstone’s Law of Comparative Judgment asserts that responses are normally distributed about a most frequent response[l7]. The frequency of error in making pairwise choices would depend on the locations of the members of the pair on the preference scale and their discriminal dispersions. Scales which are adequate to represent the preferences of any member of the population can be constructed on the basis of aggregate data only if the differences among individual choices result from random variation. The number of errors in predicting individual pairwise choices may be large, even for valid scales, if some of the alternatives are located close to one another on the preference scale. If a population contains a mixture of individuals with two or more distinct preference scales the result of simple aggregation is likely to be a scale which cannot adequately represent any individual. Thurstone’s law provides a basis for evaluating the validity of a single scale obtained by aggregating individual scales. The collective model determines the location of alternatives on a preference scale and provides a basis for predicting pairwise choices. The member of a pair which ranks higher on the preference scale should be preferred. The frequency of errors in predicting pairwise choices should be inversely related to the distance separating the alternatives on the scale. If two alternatives are widely separated, the one of lower rank should be selected by relatively few respondents. These respondents increase in number as scale separation between alternatives decreases. The idea of a monotonic relation between pairwise distance and relative frequency of choice is a basis for some methods of scaling. In this case it is used to check for the validity of a scale which is derived by aggregating individual scales.

PREFERENCE ORDERINGS FOR TRAVEL TIME AND USER CM

Models developed along these lines can have practical value in planning applications as well as theoretical interest. Applications in planning require the models to be calibrated, preferably with modest quantities of data. It is also important to examine the level of error introduced by aggregation of individuals. The example presented here demonstrates how the models can be fitted by means of relatively economical data surveys. The problem of aggregation also is examined for a relatively homogenous population. Models of individual and collective preferences were fitted and evaluated for data gathered in a survey of rail commuters in three North Shore suburbs of Chicago in January of 1976.Respondents’ pairwise preferences were gathered for a set of nine travel alternatives. These alternatives were presented as combinations of two attributes; travel time and fare level, each of which assumed one of three distinct values. The levels of attributes were 40. 60 and 80 min of travel time and $1.20, $1.50 and $1.80 for fare levels. These values were close to those actually experienced by the respondents but covered a sufficrent range to have been perceived as different. The number of alternatives and attributes included in the survey is small and the scope of the survey, in terms of the number and location of respondents, is modest. However, the survey methods were designed to be compatible with larger scale sample surveys.

JAKUBS

The data survey

The number of responses which must be elicited from each subject is a major problem in gathering data on pairwise choices. Even for the nine alternatives used here, the number of responses necessary to obtain all pairwise preferences is 36. The number of pairs increases in proportion to the square of the number of alternatives so including many more alternatives makes it unreasonable to attempt to obtain full responses from a large number of individuals. The number of questions was reduced in this survey by applying a dominance assumption. This a&umption states that a respondent, when confronted with a choice between two alternatives. would always prefer the one with shorter travel time if its fare level were the same or lower. Similarly, a respondent would always prefer a cheaper alternative were the travel time the same or shorter. This left 9 choice tasks at issue: situations where one alternative was cheaper but the other offered a shorter travel time. Preferences for these nine pairwise choices were elicited by means of a questionnaire. Respondents were asked to select the preferred member of each of 9 pairs of alternatives. The questionnaire consisted of a stamped postal card and its brevity was expected to contribute to a high response rate. In all, 144 questionnaires were distributed on three separate mornings to persons who were beginning rail commuting journeys at the nearby stations of Highland Park, Lake Forest and Lake Bluff, Illinois. Eighty-three questionnaires were returned. Of these, 67 had been completed fully. The 16 incomplete questionnaires were not used in the analysis. Results for individuals

The pairwise choices made by each respondent were resolved into a rank ordering by means of the algorithm MDPREF. The conjoint measurement algorithm, MONANOVA, was applied in each case to obtain a combination rule to account for the ordering of the alternatives as a function of travel time and fare level. The result is a scale value, Sir,for each alternative, which is the sum of a coefficient for the particular travel time, ti, and a coefficient for the particular fare level, cj. The scale value S, is monotonically related to the rank ordering of alternatives for the individual. Eighteen different response patterns occurred among the 67 respondents. On the whole, respondents favored alternatives with shorter travel times to those with lower fares. The most frequent response, shared by 28 of the respondents, was one in which the shorter travel time is always selected regardless of cost. Two respondents always favored the cheaper mode. The responses made by the remaining 37 subjects reflect consideration of both fare level and travel time. A summary measure of the importance of an attribute in a respondent’s choices is available as the proportion of the variance of scale values accounted for by variation in the coefficients of that attribute. That is, the variance of the scale values is equal to the sum of the variance of the coefficients for each attribute:

C C (Sij- S)*= C

(t; - T)‘+ 2 (Cj - CT)‘,

and the proportion of variation in the scale values resul-

Urban

travel

alternatives:

models

for individual

ting from variation in travel time is &, where 2, = 2 (fi - 7)’ c c (Sij-Q?. / A frequency diagram of the proportion of the variance in scale values accounted for by variation in the valuation of travel time is given in Fig. 1.

and collective

269

preferences

a chi-square test of the significance of differences between empirically observed preferences and preferences which are expected theoretically from the scale values obtained previously. This test was undertaken for the scale in Fig. 2. The differences were significant at the 0.01 level, leading us to reject the notion that the obtained scale accurately depicts preferences of the group in total. Since the derived

2% f

24-

E 20-

E t

16I

1 III, Ill,1 .9

.8

.7

,,I

.6

I .5

I

Proportion of Variance aecoantsd Fig. 1. Frequency

Results

for

aggregations

diagram

for the proportion

of pairwise

choices

Mo,l50)

3.799

(60,120)

2.718

(40,180)

2.306

(60,150)

1.421

(80,120)

.686

(60,180)

0 t (80,150) Fig. 2. The Thurslone

Scale based on aggregation pairwise choices.

.i

forby

.2

.I

at the level of

.O

travel time

of the variance of the scale values accounted travel time coefficient.

The entire set of 603 pairwise choices given by the 67 respondents can be used to derive a preference scale and the resulting scale values can be explained on the basis of a conjoint measurement model. An interpretation of Thurstone’s Law of Comparative Judgment was employed in an attempt to develop a single scale, common to respondents as a group[ 171.The assumption was made that a given stimulus does not always evoke the same discriminal process; instead, such processes are distributed normally about a “modal discriminal process”. In this way, the scale depicted in Fig. 2 was obtained. Seven stimuli are shown in the scale. The locations of the remaining two could not be ascertained, because a dominance assumption had been made to generate preference data for these two stimuli. This procedure has a goodness-of-fit test associated with it. The test is particularly sensitive to heterogeneity of preferences within the group[ 17, p. 541.Briefly, this is

4.307

1

1

A

for by variation

in the

scale probably is invalid the conjoint measurement analysis was not carried out for this case. Results

for

aggregating

indkidual

preference

functions

Four methods of aggregating individual preference functions were applied to obtain collective preference functions. The result in each case is a set of coefficients obtained by aggregating individual coefficients. The four sets of coefficients appear in Table I and the associated preference scales are shown in Fig. 3. The first collective preference function is simply the modal, or most frequent, response. The most frequent response is of some interest because it represents the desires of a simple majority. In this case. it corresponds to a simple kind of preference in which the faster alternative is always selected regardless of fare level. The second collective preference function is obtained by averaging the coefficients over all individuals. The resulting function gives equal weight to the preferences of all individuals in the sample. The third and fourth models are based on weighted averages where the weights are used to reduce the influence of deviant individuals on the collective preference. The third model is calculated by weighting each individual’s coefficients by the rank order correlation of the individual’s preference ordering with the most frequent preference ordering. This reduces the influence of individuals who deviate from the most frequent response. The coefficients for the fourth model also are obtained as weighted averages where the weights for each individual are average rank correlations of the individual’s preference ordering with all other preference orderings. This reduces the effect of individuals whose preferences deviate from those of the group as a whole. The various scales can be evaluated in terms of their success in predicting the 603 pairwise choices which make up the set of responses but there was little difference among the four on these grounds. The predicted choices were the same with one exception: the three models based on averaging differed from the most frequent response in predicting the choice of an al-

270

JOHN

Table

I. Conjoint

YODEL

1 - MOST

ODI.ASI)

measurement FREQUENT

coefficients

Fare

Tine

Level,

MODEL

2 -

60 Minutes

1.20

1.50

.6250

.oooo

1 60 I

1.5688

Time

Level,

MODEL

WEIGHTED

BY

CORRELATION

S

Tine

Level,

.6250

80 Minbtes -1.6602

1.80

60 Minutes

.7466

.0247

BY AVERAGE

-1.6111

1.80 - .7712

.0667

1.20

1.50

.7419

.0252

1

80 Minutes -7.5785

1.a

$

- (4C. 120)

(40. 120)

RESPONSE

CORRELATION

60 Minutes

1.4921

FREQUENT

CID Minutes

.06522

1.50

WE:GHTED

- .8231

jlITH MOST

1.20

40 Minutes

Fare

1 I

.0257

1.5258

4 - AVERAGC

Travel

tlicutes

1.50

50 Minutes

Fare

-

S

3 - AVERAGE

Travel

I .a0

.3710

1.7975

MODEL

-1.8750

,IMPLE AVERAGE

Time

Level,

functions

5

1.20 Fare

preference

80 Minutes

.oooo

1.8750

40 Minutes Travel

for 4 collective

RESPONSE

40 Minutes Travel

and JOHN JAKUBS

-

.7664

- (40,1201

- (40, 120)

- (40.150)

- (40.15cl

- (40. 150) - (40.150) - (40, 180) (60, 120)

_ (60.120) - (40, 180)

(60, 150)

- (60,150)

- (60, 150)

1 (60.180) (80,120)

- (60.160) - k30.120)

- (80,150

- 80,150)

- Bc,180)

- (80, 180)

- (40, 180)

- (60,120)

- (60,150)

- (60,BOl

_ (6G.120) - (40.180)

- @30I20)

- (80. 150)

-

P30,180)

@0,180)

Fig. 3.

Scales for 4 collective

ternative with 60 min of travel time and a fare level of $1.20 over one which offered a 40 min travel time at $1.80. There were no differences in pairwise predictions among the average and weighted average models. The total number of incorrectly predicted choices was nearly the same for all four models. The most frequent response

preference

functions.

predicted 18.4% of the pairwisc choices incorrectly. The models using averaging predicted 18.1% of the choices incorrectly. There was little apparent difference between the collective preference scale based on simple averages and the two based on weighted averages. The differences

Urban travel alternatives:

Model

Scale

Separation

Scale

Separation

models for individual

and collective

preferences

I

Model 2

Fig. 4. Diagrams of error frequency

which do exist were important. however. The scale based on simple averages failed to achieve a monotonic relation between the frequency of error for pairwise choices and the scaled distances between the members of pairs. This occurred because the set of respondents contained a sizable minority who selected cheaper alternatives rather than shorter travel times. The weighted averages were less influenced by these deviant individuals and came much nearer to achieving a monotonic relation between error frequency versus scaled distances are shown in Fig. 4. CONCLL’SIONS

The conjoint measurement model provides a useful approach to travel preferences and travel behavior because it allows preferences for alternative modes to be explained on the basis of generic attributes associated with each mode. The models have the capacity to provide important insights into the choice-making of commuters by identifying the attributes, such as speed or user cost, which are of greatest importance in the mode choice decision. In a planning context, the models may be used to select those attributes which might be m;nipulated in order to induce major changes in commuters’ mode choices. The possible heterogeneity of preferences appears to be the major obstacle to larger scale applications of these methods. The sample of commuters examined here can be presumed to be fairly homogeneous in terms of their home and work locations, income and daily commuting experience and their responses are dominated by preferences for quicker journeys over lower fares. Their responses are varied enough, however, to preclude construction of valid collective preference models based on aggregation of pairwise choices or simple averaging of individual preference functions. Collective preference functions which are associated with only modest amounts of error can be constructed in this case as weighted averages where the weights reduce the influence of deviant individuals. Weighting methods may be insufficient in the general case. however, and it may

be necessary to disaggregate the population into homo-

171

Scale

Separation

Scale

Separation

vs scale separation.

geneous subgroups and develop separate preference scales for each subgroup. REFERENCES I. D. Brand, Approaches to travel behavior research. Trunspn Res. Record, No. 569, pp. 12-33 (1976). 2. P. Burnett, Disaggregate behavioral models of travel decisions other than mode choice. Transpn Res. Board. Special Report, No. 149. pp. 207-222 (1974). 3. R. Dobson. Towards the analysis of attitudinal and behavioral responses to transportation system characteristics. Transpn 4, 267-290 (1975). 4. C. H. I.ovelock. Modelling rhc modal choice decision process. Transpn 4. 253-275 (1975). 5. G. C. Nicolaidis and R. Dobson. Disaggregate perceptions and preferencesin transportation plan&g.-Tranipn l&r. 9. 279-295 (1975). K. J. Lancaster, A new approach to consumer theory. _I. po’olit. Econ. 74, 132-157 (1966). K. J. Lancaster, Consumer Demand a New Approach. Columbia University Press, Sew York (1971). R. D. Lute and J. W. Tukey. Simultaneous conjoint measurcment: a new type of fundamental measurement. .I. iMath. Psycho/. 1, 1-27 (1964). A general theory of polynomial conjoint 9 .4. Tversky, measurement. 1. Math. Psycho/. 4. I-20 (1%7). 10 R. Quandt and W. Baumol, The demand for ahstrdct transport modes: theory and measurement. J. Reg. Sci. 6, 13-26 (1966). 11. W. R. Allen and A. Isserman. Behavioral modal split. High Speed Grortnd Transpn J. 6. 179-199 (1972). 12 P. R. Stopher and A. H. Meyberg. Travel demand estimation a new prescription. Trafic Engng Control 15. 879-884 (19741. 13. K. J. Button, The use of economics in urban travel demand modelling: a survey. Socio-Econ. Plan. Sci. 10.57-66 (1976). 14. T. A. Domencich and D. McFadden. Urban Truce/ Demand, A Behac;ioral Anolgsis. North Holland. Amsterdam (1975). 15. J. J. Chang and J. D. Carroll, How to use MDPREF, a computer program for multidimensional analysis of preference data, mimeographed. Bell Laboratories, Murray Hill, New Jersey (1%9). 16. J. B. Kruskal. Analysis of factorial experiments by estimating monotone transformations of the data. 1. Roy. Sratisl. Sue. R27. 251-263 (1965). 17. A. L. Edwards, Techniques of Attitude Scale Construction. Appleton-Century-Crofts, New York (1957).